Visualizing Large Complex Data is Difficult

Problem: Modern data sets are growing in size and complexity

• Goal: Understand key relationships in large complex data sets

• Difficulty: Large data volume

  • Modern computational systems have massive capacity
    
  • Example: Use map-reduce algorithms on cloud clusters

• Difficulty: Large numbers of variables

  • Huge number of variables with many potential relationships
    
  • This is the hard part!

Limitation of Scientific Graphics

All scientific graphics are limited to a 2-dimensional projection

• But, complex data sets have a great many dimensions

• We need methods to project large complex data onto 2-dimensions

• Generally, multiple views are required to understand complex data sets

  • Don’t expect one view to show all important relationships
    
  • Develop understanding over many views
    
  • Try many views, don’t expect most to be very useful

Scalable Chart Types

Some chart types are inherently scalable.

• Bar plots: Counts can be computed; e.g. use map-reduce
  
• Histograms: Data is binned in parallel
  
• Box plots: Finding the quartiles is a scalable counting process
  
• KDE and violin plots: Similarly to the box plot, using kernel density estimation

Over-plotting

Over-plotting occurs in plots when the markers lie one on another.

• Common, even in relatively small data sets
  
• Scatter plots can look like a blob and be completely uninterpretable
  
• Over-plotting is a significant problem in EDA and presentation graphics

Dealing with Over-plotting

What can we do about over-plotting?

• Marker transparency: so one can see markers underneath; useful in cases with minimal overlap of markers
  
• Marker size: smaller marker size reduces over-plotting within limits
  
• Adding jitter: adding a bit of random jitter to variables with limited number of values

Example of Overplotting

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Use Transparency, Marker Size, Downsampling

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Use Transparency, Marker Size, Downsampling

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Other Methods to Display Large Data Sets

Alternatives to avoid over-plotting for truly large data sets

• Hex bin plots: the 2-dimensional equivalent of the histogram
  • Frequency of values is tabulated into 2-dimensional hexagonal bins
    
  • Displayed using a sequential color palette
• 2-d kernel density estimation plots: natural extension of the 1-dimensional KDE plot
  • Good for moderately large data
• Heat map: values of one variable against another
  • Categorical (count) or continuous variables
    
  • Carefully choose color pallet, sequential or divergent
• Mosaic plots: display multidimensional count (categorical) data
  • Uses tile size and color to project multiple dimensions
    
  • 2-d equivalent of a multi-variate bar chart
• Dimensionality reduction: we will discuss this later in the course

Hexbin Plot

Countour Plot

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Other Methods to Display Large Data Sets

Sometimes a creative alternative is best

• Often situation specific; many possibilities

• Finding a good one can require significant creativity!

• Example, choropleth for mutli-dimensional geographic data

• Example, time series of box plots

Time Series of Box Plots

Displays for Complex Data

How can we understand the relationships in complex data with many variables?

• Arrays of plots: subsets show relationships in a complex data set

• Pairwise scatter plots: matrix of all pairwise combinations of variables

  • Project additional dimensions with plot aesthetics
    
  • pairwise scatter plots can be created for subsets of large and complex data sets.

• Faceting: uses values of categorical or numeric variables to plot subsets

  • Subsets are displayed on an array of plots
    
  • Typically use axes on same scale to ensure correct perception of relationships
    
  • Faceting goes by several other monikers, conditional plotting, method of small multiples, lattice plotting

• Cognostics: sort large number of variables to find important relationships

Arrays of Plots

Display multiple plot views in an array or grid

• Create an array of plots which project multiple related views of data relationships
  • Organize axes to give multi-dimensional view
• Example, scatterplot with kde plots on the margins
  • Supported by Seaborn jointplot

Scatter Plot Matrix

Scatter plot matrix used to investigate relationships between a number of variables

• Key idea: D+-isplay a scatter plots of each variable versus all other variables
  • Primarily EDA tool
    
  • Conveys lots of information - requires study!
• Each pairwise relationship is displayed twice
  • Two possible orientations
    
  • Or two different plot types
• Can place histograms and KDE plots on diagonal

Scatter Plot Matrix

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Facet Plots

Facet plots revolutionized statistical graphics starting about 30 years ago

• Facet plots extend the number of dimensions projeted onto 2-d plot surface

• Key idea: Create array of plots of subsets of the data

  • Create subsets using a group-by operation on other variables
    
  • Lay out grid of plots on same axis by row and column grouping variables
    
  • Display same plot type for each group
    
  • Can add specific aesthetics, etc.

Facet Plots

Like many good ideas facet plotting was invented serveral times

• Multiple contemporaneous inventors and names
  • Tufte, 1990, introduced method of small multiples
    
  • Cleveland, 1992, introduced trellis plotting
    
  • Also known as conditioned plots
• Most packages use term facet plot

Facet Plot with Weather by Season

Congnostics

How can we visualize very high dimensional data?

• Modern data sets have thousands to millions of variables

  • Cannot possibly look at all of these

• Idea: need to find the most important relationships

• Use a cognostic to sort relationship

  • Cognostic is a statistic to sort data
    
  • Sort the variables or relationships by the cognostic
    
  • Plot relationships with most interesting cognostic

• Idea originally proposed by Tukey, 1982, 1985

Cognistic: Counties With Fastest Rate of Housing Price Increase

## C:\Users\asano\ANACON~1\lib\site-packages\pandas\core\indexing.py:1745: SettingWithCopyWarning: 
## A value is trying to be set on a copy of a slice from a DataFrame.
## Try using .loc[row_indexer,col_indexer] = value instead
## 
## See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
##   isetter(ilocs[0], value)

## 0    DC
## 1    WY
## 2    ND
## 3    MT
## 4    OK
## 5    VT
## 6    MI
## 7    MN
## Name: entity_name, dtype: object

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Summary

We have explored these key points

• Proper use of plot aesthetics enable projection of multiple dimensions of complex data onto the 2-dimensional plot surface.
  

• All plot aesthetics have limitations which must be understood to use them effectively
  

• The effectiveness of a plot aesthetic varies with the type and the application

• Visualization of modern data sets, growing in size and complexity

• Visualization limited by 2-dimensional projection

• Goal: Understand key relationships in large complex data sets

• Difficulty: Large data volume

  • Modern computational systems have massive capacity
    
  • Example: Use map-reduce algorithms on cloud clusters

• Difficulty: Large numbers of variables

  • Huge number of variables with many potential relationships
    
  • This is the hard part!